Why did you apply to our company?
Here's a chance to demonstrate the research you've done on the company and to communicate how your individual skills, experience, or background can contribute. Try to be as specific as you can about what you've learned about the company and how you, in particular, can help it.
I don't think with your experience and background you are capable of doing this job. What do you think?
Unless it is a relatively odd situation, it is not likely that you would even be interviewing with this person if you weren't capable of doing the job. This is more of a test to see how you respond rather than exactly what you say. But something along the lines of, "The people I have worked for in the last two jobs thought I was under qualified before they hired me. But I performed very well on both. I am an overachiever and have always been able to perform well beyond my apparent capabilities." Then tell a story if appropriate.
Why should I hire you?
"Because I can do the job, I'm a hard worker, people like me, I'm not a great risk, and we can come to a conclusion about money."
Why have you not been promoted sooner? If you're so good, why haven't you been promoted?
Don't let a question like this get "under your skin." You can never let a question like this make you mad, and it is best not to show irritation. Simply state that in the organizations that you had been in there was a "bottleneck" of very tenured people available for the few promotions that came up. Although you knew that the quality of your work deserved the opportunity to be promoted, the probability was very unlikely simply because there were too many other people looking to be promoted who had been with the company longer than you had. In fact, this is one of the very reasons that you were looking to change jobs.
How does our position compare with the other opportunities you are currently interviewing for?
Be honest and fairly brief. It is always a good idea to let an interviewer know that you were being considered by other organizations. If you feel comfortable in mentioning who the organizations are, that's fine. Always be sure to say something like, "Taking into consideration everything I know about the other opportunities that I am interviewing for, the position here with you seems to be a little bit better match." Just be sure that you have good reasons for saying that.
You really don't have as much experience as we would like; why should we hire you?
The answer to a question like it is simple. "You know, it's very interesting, and every job I've ever had I never went in to the job having all of the experience that my previous employers wanted. In fact, I went into three of them where I was hired simply because I had more potential than any other candidate. As you can see, I have been successful in every position that I've been in even though I had no experience before I started. Some people catch on to things more quickly than others and I happen to be one who is blessed that way. I'm a quick learner and I've been able to pick up the things that I didn't necessarily have any experience with and do extremely well."
Have you ever "failed" in a job?
Answer this serious question with a "light approach." Say something along the lines of, "Well, I'm like a ballplayer that never really lost—he just ran out of time. Even the very few things that I look back on and others might see as 'failures,' I really see as setbacks. Like most people, not everything that I've ever done has turned out as perfectly as I would have liked. But even when it didn't, I've learned from it."
If you could, what would you change about the position you're interviewing for?
You can begin the question here just something like, "Based on most everything that I know, it seems that what you are asking for in the function of the position is reasonable. I really don't know enough about the position to know what might or could be changed."